Calculus | Senioritis

John Rhodes
July 29, 2023
Calculus

Understanding Cusps in Mathematics | Exploring the Sharp Corners and Sudden Bends on Curves

What does a cusp look like? In mathematics, a cusp refers to a point on a curve where the curve has a sharp corner or bends suddenly...

John Rhodes
July 29, 2023
Calculus

The Importance of Differentiability | Understanding the Conditions for Derivative Existence in Mathematical Graphs

When does a derivative not exist at ‘x’ (with a graph)? A derivative does not exist at a certain point ‘x’ on a graph when the tangent...

John Rhodes
July 29, 2023
Calculus

The Quotient Rule | Understanding and Applying Calculus’ Fundamental Tool for Solving Problems

Quotient rule? In calculus, the quotient rule is a formula used to find the derivative of a function that is expressed as the quotient of two other...

John Rhodes
July 29, 2023
Calculus

Exploring the Fundamentals | An In-depth Guide to Limits in Mathematics

Limit In mathematics, the concept of a limit is fundamental in approaches towards understanding the behavior of a function or sequence as its input (or index) approaches...

John Rhodes
July 29, 2023
Calculus

The Mean Value Theorem | Understanding Calculus and the Relationship Between Derivatives and Average Rates of Change

If the appropriate conditions are satisfied, what does the Mean Value Theorem guarantee? The Mean Value Theorem (MVT) is a fundamental theorem in calculus that guarantees the...

John Rhodes
July 29, 2023
Calculus

Understanding the Mean Value Theorem | Conditions and Application in Calculus

What conditions must be to satisfied for the Mean Value Theorem to be valid? The Mean Value Theorem (MVT) is a theorem in calculus that guarantees the...

John Rhodes
July 29, 2023
Calculus

Exploring the Chain Rule in Calculus | Derivative of a^u with respect to x

d/dx(a^u) To find the derivative of the function f(x) = a^u with respect to x, where a is a constant and u is a function of x,...

John Rhodes
July 29, 2023
Calculus

The Chain Rule | Finding the Derivative of e^u with respect to x

d/dx(e^u) To find the derivative of the function f(u) = e^u with respect to x, we can use the chain rule To find the derivative of the...